Bounding the regularity of subschemes invariant under Pfaff fields on projective spaces

On invariant notions of Segre varieties in binary projective spaces

Invariant notions of a class of Segre varieties S(m)(2) of PG(2m − 1, 2) that are direct products of m copies of PG(1, 2), m being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains S(m)(2) and is invariant under its projective stabiliser group GS(m)(2). By embedding PG(2 m − 1, 2) into PG(2m − 1, 4), a basis of the latte...

Projective Invariant Metrics for Einstein Spaces

On a Metric on Translation Invariant Spaces

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

Bounding the Degree of Solutions to Pfaff Equations

We study hypersurfaces of complex projective manifolds which are invariant by a foliation, or more generally which are solutions to a Pfaff equation. We bound their degree using classical results on logarithmic forms.

Reducibility mod p of integral closed subschemes in projective spaces – an application of arithmetic Bézout